Three-phase contact wetting perimeter

The presence of the transition zone between a drop or a bubble and thin liquid interlayers can be described in terms of line tension, x, a concept first introduced by Gibbs (see for example [22]). In the case of surface tension, the transition zone between the liquid and vapor is replaced by a plane of tension with excess surface energy, y. By analogy, the transition zone between a drop or a bubble and the thin liquid interlayer may be replaced by a three-phase contact line with an excess linear energy, x. In contrast to surface tension defined always as positive, the value of the line tension may be positive and negative. When positive, it contracts the wetting perimeter, whereas the perimeter expands if the line tension is negative [33-36]. 

FIGURE 3.2 Spreading of a spherical droplet. At h > fr, the spherical droplet profile is not distorted by the hydrodynamic flow t < is the radins of action of the disjoining pressure r t) is the macroscopic wetting perimeter (the apparent three-phase contact line) R(t) is the tme microscopic wetting perimeter 0(f) is the dynamic contact angle and H(t) is the drop apex. 

Because there can be degrees of wetting of particles at an interface, another quantity is needed. The contact angle, 6, in an oil—water—solid system is defined as the angle, measured through the aqueous phase, that is formed at the junction of the three phases. Whereas interfacial tension is defined for the boundary between two phases, the contact angle is defined for a three-phase junction. If the interfacial forces that act along the perimeter of the drop are represented by the interfacial tensions, then an equilibrium force balance can be written as... 

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